The research objective is to develop data-analytic statistical methods for samples of highly categorized or cross-classified incidence counts, such as reported frequencies of new cancer cases classified by site of primary tumor and by reporting institution. Such data characteristically varies erratically over categories, due to sampling variability, and exhibits many categories with very low or zero counts. Smoothing functions will be developed to estimate the incidence rate in a category by making use of neighboring category counts as defined by context-suitable metrics. The new smoothing functions will be adaptive in being based on empirical Bayes inferences on the degree of local smoothness among the unobserved true incidence rates. Extensive automatic computing will be necessary in the construction of functions and their verification for data-analytic use, both by simulated sampling and by sampling large data sets treated as populations. The methods developed will be immediately applicable to probabilistic medical diagnosis.